The mass number is the total number of protons and neutrons in the atom. But this is more of a maths question rather than chemistry.
Let's assume there are x units of the isotope with mass number m
y units of the isotope with mass number m+1
z units of the isotope with mass number m+2
So the mean would be (xm + y(m+1) + z(m+2)) / (x+y+z) [Mean = Total sum/Total quantity]
which is equal to m+0.5 [Given in question]
Solving this we get, 0.5(x - y - 3z) = 0=> x = y+3z -----------equation (1)
Now we can put values of y and z and get x. There can be infinitely many values of x, y and z.
Here amongst the options, we can see that option (b) matches this criterion.
To be precise, if we take a constant k, then x=4k, y=k and c=k satisfy equation (1).
We can also see that option (a) and option (c) don't satisfy equation (1)
So amongst the options, option (b) is the answer.
As a check, if we take other ratios which satisfy equation (1) they can also be an answer to the question.
e.g. 7:1:2 => x=7k, y=k, z=2k
Now the mean would be, (xm + y(m+1) + z(m+2))/(x+y+z)
Putting the values,
(7km + k(m+1) + 2k(m+2))/(7k + k + 2k)
= (10 km + 5k)/(10k)
= m + 0.5
So 7:1:2 can also be a ratio which satisfies the given criterion.